Distributed Minimum Spanning Tree Maintenance for Transient Node Failures

In many network applications, the computation takes place on the minimum-cost spanning tree (MST) of the network G; unfortunately, a single link or node failure disconnects the tree. The ALL NODES REPLACEMENT (ANR) problem is the problem of precomputing, for each node u in G, the new MST should u fail. This problem has been extensively investigated for serial and parallel settings, and efficient solutions have been designed for those environments. The situation is surprisingly different in distributed settings. In fact, no distributed solution exists to date which performs better than the brute-force repeated application of MST construction. In this paper, we consider for the first time the problem of computing all the replacement minimum-cost spanning trees distributively. We design a solution protocol, and we prove that the total amount of communication exchanges taking place is O(n), each exchange using at most O(n) data items. Hence, the total amount of data items communicated during the computation (the data complexity) is O(n^2). We also show how the simpler problem ALL EDGES REPLACEMENT (AER) dealing with single edge failures, which can be solved with the same costs using some existing techniques. Also for the AER problem, efficient solutions exist in the serial and parallel setting but, prior to this work, no distributed solution other than brute force was known.